High gain null-balance servo system

ABSTRACT

A multi-loop, high-gain null-balance servo measuring system having low sensitivity to parameter variations and comprising a pre-amplifier, a post-amplifier and a DC motor for driving an adjustable circuit element. The circuit element is driven by the motor in response to an error signal equal to the difference at null between an unknown input signal and a restoring signal provided by the overall system or outer loop feedback which represents the position of the adjustable circuit element. Reactive means are provided for establishing at least one inner loop feedback path for applying velocity and acceleration signal components to the input of the post-amplifier.

United States Patent [191 MacMullan 1 May 8, 1973 154] HIGH GAINNULL-BALANCE SERVO SYSTEM [75] Inventor: Samuel J. MacMullan, Newtown,

21 Appl. No.: 240,637

Related US. Application Data [63] Continuation-impart of Ser. No.126,667, March 22,

1971, abandoned.

3,013,194 12/1961 Cary ..318/6l8 3,048,759 8/1962 Howard.. ..318/6163,373,675 3/1968 Best ..318/616 X 3,460,013 8/1969 Gaylor........318/6l6 X 3,512,060 5/1970 Floyd ..3l8/6l6 X Primary Examiner-Benjamin Dobeck AttorneyRichard E. Kurtz et a1.

[57] ABSTRACT A multi-loop, high-gain null-balance servo measuringsystem having low sensitivity to parameter variations and comprising apre-amplifier, a post-amplifier and a DC motor for driving an adjustablecircuit element. The circuit element is driven by the motor in responseto an error signal equal to the difference at null between an unknowninput signal and a restoring signal provided by the overall system orouter loop feedback which represents the position of the adjustablecircuit element. Reactive means are provided for establishing at leastone inner loop feedback path for applying velocity and accelerationsignal components to the input of the post-amplifier.

29 Claims, 17 Drawing Figures I [52] U.S. Cl ..318/616, 318/618 [51]Int. Cl. ..G05b 5/01 [58] Field of Search ..318/6l5,616,617, 318/618,609, 610

[56] References Cited UNITED STATES PATENTS 2,549,829 4/1951 Lilja..318/6l6 2,913,649 11/1959 McKenney et al ..318/6l6 X 10 2 v 8; 32 30 2K W\o-| PATENTEDHAY 81973 SHEET 1 BF 7 PATENTED MAY 8 7 SHEET 3 OF 7 Pi.5d

P IENTEnHAY'ws SHEET u 0F 7 PI .5b

ACC. VOLTAGE HIGH GAIN NULL-BALANCE SERVO SYSTEM RELATED APPLICATIONSThis application is a continuation-in-part of application Ser. No.126,667, filed Mar. 22, 1971 and now abandoned.

BACKGROUND OF THE INVENTION input signal.

Such systems comprise a pre-amplifier and associated circuitry forgenerating an error signal representing the difference at null betweenan unknown input signal and a restoring signal in the form of a feedbacksignal from an adjustable circuit element. The amplified error signalfrom the pre-amplifier is then applied to a post-amplifier having anoutput connected to a DC motor which is mechanically coupled to theadjustable circuit element. The position of the adjustable circuitelement is represented by the restoring signal. The restoring signal isapplied to the circuitry for generating an error signal through anoverall system or outer feedback loop.

In many cases, the small signal response of the prior art systems hasbeen dependent upon parameters of the DC motor and the adjustablecircuit element. More particularly, the dominant time constants andhence the dynamic performance of the system have varied with changes inmotor time constants and coefficients such as a motorvoltage-to-velocity coefficient, k a motor time constant 1-, andadjustable circuit element parameters. Thus the dynamic performance ofthe system was affected by any replacement of motors or variations inthe motor parameters. Even changes in load mass due to the mounting ofaccessories will affect the dynamic performance of the system. As aconsequence, adjustable resistors and capacitors have been utilized tomaintain dynamic performance by permitting suitable circuit adjustments.

In some prior art systems, inner feedback loops have been provided. Afirst inner loop provides a direct coupled velocity feedback path to theinput of the post-amplifier. A bridge is used to derive a velocitysignal directly from the motor. A second inner loop provides a directcoupled motor voltage feedback path. The primary disadvantage of thissystem is due to the fact that the bridge must be unbalanced by acertain amount so that variations in parameters do not result in apositive feedback component that increases with frequency therebycausing instability: this balance results in a feedback that isproportional to the motor current and a consequent degradation of staticgain producing excessive deadband.

Furthermore, prior art null-balance servo systems have generallydemonstrated instability when gain and damping are adjusted. Forexample, small changes in gain can lead to oscillatory transient modeson the one hand and excessively long transient modes on the other. Theseproblems are compounded by the multiplicity of ways in which gain anddamping are adjusted in any given prior art system.

SUMMARY OF THE INVENTION It is an overall object of this invention toprovide a null-balance servo system closely approximating a desiredsmall signal response.

It is a still more specific object of this invention to provide anull-balance servo system where changes in motor parameters do notsubstantially affect the small signal dynamic performance of the system.

It is another specific object of this invention to provide anull-balance servo system where changes in load mass due to the mountingof accessories do not substantially affect the small signal dynamicperformance.

It is a further specific object of this invention to provide anull-balance servo system where changes in parameters do not requiresignificant adjustments in circuit components to maintain dynamicperformance.

It is a still further specific object of this invention to provide anull-balance servo system without excessive deadband.

In accordance with these and other objects of the invention, ahigh-speed null-balance servo system embodying the invention comprisesmeans for producing an error signal related to the difference between aninput signal and an overall system feedback signal for restoring balanceto the system, a DC pre-amplifier for amplifying the error signal, and'aDC post-amplifier coupled to the output of the pre amplifier. A meansfor producing feedback signals comprises a DC motor and associatedcircuitry connected to the output of the post-amplifier and anadjustable circuit element mechanically coupled to the motor. An outerloop feedback means couples the adjustable circuit element to the meansfor producing an error signal. An inner loop feedback means includingreactive means couples the means for producing feedback signals to theinput of the post-amplifier so as to apply velocity and the accelerationfeedback signal components to the input of the post-amplifier, theacceleration feedback signal component being substantially free of thevoltage drop across the motor resistance.

In one specific embodiment of the invention, a system is provided havinga higher order than the order of the sub-loop including thepre-amplifierand circuitry for generating an error signal. This achieves reducedsensitivity to parameter variations for the small signal response to agiven input since a wider stability margin can exist in lower ordersub-loops. Thus, for example, variations in pre-amplifier gain orbandwidth causes reduced alterations of nominal system frequencyresponses.

The system of this specific embodiment includes an outer or first loopproviding overall system feedback and second and third loops formingsub-loops within the first loop. A proportional plus derivative meanscoupled to the output of the adjustable circuit element interposedbetween the adjustable circuit, element andthe means for producing theerror signal produces the overall system feedback signal including avelocity component. A reactive feedback means is coupled between theproportional plus derivative means and the input of the DCpost-amplifier to establish the second and third sub-loops where thesecond sub-loop includes the pre-amplifier and the third sub-loopincludes the post-amplifier, the motor, the adjustable circuit element,the proportional plus derivative means, and the reactive feedback meansand where the third sub-loop acts like an integrator with respect to thesecond subloop.

In another specific embodiment, the subsystem defined by an inner loopproviding velocity feedback to the DC post-amplifier is made stable bymaking the acceleration feedback gain depend on the tachometriccoefficient of the motor, rather than the resistance of the motor. Thevelocity feedback gain depends only on stable feedback subsystems thatare driven by the adjustable circuit element. Hence, the bandwidth ofthe aforesaid inner loop which is proportional to the ratio of gains ofthe velocity feedback loop and the acceleration feedback loop in astable quantity. As a result, parameter variations have very littleeffect on the system dynamic performance even though the bandwidth ofthe subsystem may be of the same order as that of the overall system. Inother words, the inner loop can provide a dominant time constant as aresult of this improved stability. This is a particular advantage insystems where inner loop bandwidth is restricted. For example, innerloop bandwidth may be limited by compromising gearing back lash andmechanical resilience for the sake of economy. This is also an advantagein other servo systems that have tight coupling between the motor andthe load. In such systems, the system bandwidth is still limited by thebandwidth that can be achieved in the higher bandwidth subsystem.

This specific embodiment also reduces the delays in response for smallerror signals by permitting a reduction in the feedback of the motorvoltage derivative from the use of acceleration feedback. The motorvoltage is proportional to the torque applied to the load when the loadis at rest. When the derivative of this component is fed back,sufficient integrating time must elapse before sufficient torque isachieved to start the load in motion. By minimizing this feedback,reduced delays in response are achieved.

In this specific embodiment, the reactive means of the inner loopfeedback means is coupled between the input to the post-amplifier andthe circuitry associated with the DC motor as well as the adjustablecircuit element. Separate reactive feedback paths may be provided forboth the acceleration feedback and the velocity feedback from thecircuitry associated with the DC motor and the adjustable circuitelement. As an alternative, a combined reactive feedback path may beprovided from the circuitry associated with the DC motor and theadjustable circuit element.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic-block diagramofa null-balance servo system embodying the invention arranged toclearly show an outer loop and two sub-loops;

FIG. la is a schematic diagram of analternative reactive network whiehmay be utilized in the system of FIG. 1;

' FIG. lb is a schematic diagram of an alternative reactivenetwork whichmay be utilized in the system of FIG. 1;

FIG. 1c is a schematic diagram of a passive proportional plus derivativecircuit which may be utilized in the system of FIG. 1;

FIG. 2 is a schematic-block diagram of another system embodying theinvention also arranged so as to clearly show an outer loop and twosub-loops;

I feedback amplifier 20 and the capacitor 30. Thus the p FIG. 3 is amore detailed schematic diagram of the system of FIG. 1 in anull-balance recorder;

FIG. 4 is a more detailed schematic diagram of the system of FIG. 2 in anull-balance recorder;

FIG. 5 is a schematic-block diagram of another system embodying theinvention;

FIG. 5a is a schematic diagram of alternative cir cuitry which may beused in the system of FIG. 5 to produce a velocity feedback signalcomponent;

FIG. 5b is a schematic diagram of alternative circuitry which may beused in the system of FIG. 5 to apply a velocity feedback signalcomponent to the input of the post-amplifier;

FIG. 50 is a schematic diagram of alternative circuitry which may beused in the system of FIG. 5 to sum the signals at the input of thepost-amplifier;

FIG. 5d is a schematic diagram of alternative circuitry which may beused in the system of FIG. 5 to produce an acceleration feedback signalcomponent;

FIG. 6 is a more detailed schematic diagram of the system of FIG. 5 in anull-balance recorder;

FIG. 7 is a schematic diagram of another system embodying the invention;

FIG. 8 is a detailed schematic diagram of a typica amplifier outputcurrent gain stage for the system shown in FIG. 5; and

FIGS. 9 and 10 are detailed schematic diagrams of output stagesutilizing switching mode amplifiers.

DESCRIPTION OF PREFERRED EMBODIMENTS As shown in FIG. 1, a null-balanceservo system comprises a means for generating an error signalrepresenting the difference between an input signal and an overallsystem feedback restoring signal at a summing junction 10, apre-amplifier 12 (shown in block-diagram form as having a gain K and apost-amplifier 14 connected to a terminal of a DC motor 16 which ismechanically coupled to an adjustable circuit element 18. As theadjustable tap 18a of the adjustable circuit element 18 moves inresponse to movement of the motor 16, a feedback signal is generatedwhich is in turn applied to a feedback amplifier 20. The output of thefeedback amplifier 20 is then coupled to the summing junction 10 bymeans of the outer loop feedback means including feedback network 22(shown in block diagram form as having an attenuation factor B).

For a thorough understanding of-the preferred embodiment of theinvention, the circuit shown in FIG. 1 may be considered to consist ofthree feedback loops. The first loop is the overall or outer feedbackloop in-- eluding the summing junction 10, the pre-amplifier 12, theresistor 32, the post-amplifier 14, the motor 16, the adjustable circuitelement 18, the feedback amplifier 20 and feedback network 22. Thesecond loop is the pre-amplifier sub-loop including the summing junction10, the pre-amplifier 12, the resistor 32, the capacitor 30, and thefeedback network 22. The third loop is the post-amplifier sub-loopincluding the post-amplifier 14, the motor 16, the adjustable circuitelement 18, the

inner loop feedback means including a' reactive means in the form of acapacitor 30 completes the second and third sub-loops and'providesvelocity and acceleration feedback signal components for the input ofthe postamplifier.

In accordance with the invention, the second order system of FIG. 1 ischaracterized by first and second dominant system time constants whichdetermine the dynamic performance of the system. The first dominantsystem time constant is established by a proportional plus derivativemeans comprising an active RC filter network 24 associated with thefeedback amplifier 20 and including a resistor 26 and a capacitor 28.This is a normal lead network in the feedback path of the overall servoloop which is designated as the first loop. This network is alsoinvolved in the third loop. Post-amplifier 14, a resistor 36, acapacitor 38, the motor 16, the adjustable circuit element 18, and thefeedback amplifier 20. including the network 24 may be viewed as anamplifying device connected between 2, and e and having the capacitor 30in its feedback path. Thus it will be seen that the third loop behavesin the manner of an integrator with respect to the second loop and thesecond dominant system time constant is established by the feedbackcapacitor 30 in combination with the resistor 32 connected to anothersumming junction at the input of the post-amplifier 14. I

It can be seen from the above analysis that there is a first dominanttime constant in the third loop which is also common to the first loopand a second dominant time constant in the second loop which is alsocommon to the first loop. But these elements that make up the firstandsecond dominant time constants appear in the first or overall loop incascade and hence provide a second orderservo system.

Returning now to the third or post-amplifier loop, it is to be notedthere is a reactive feedback path from the output of post-amplifier 14to an inverting input of the post-amplifier 14 consisting of resistor 36and capacitor 38, which forms a post-amplifier integrator. The input tothe post-amplifier 14 may be connected to either the inverting or thenon-inverting input. If the circuit design calls for connection to theinverting input then the non-inverting input of the post-amplifier 14 isconnected to circuit common. This post-amplifier integrator 34 appliesan integrated error signal to the motor 16 where the gain of thepost-amplifier integrator 34 is defined as the reciprocal of theintegrator time constant which is proportional to the product R C(seconds). In accordancewith this invention, the gain of thepost-amplifier integrator 34 must be sufficiently high so that the thirdloop actslike an integrator with respect to the second or pre-amplifierloop. The third loop is also characterized by another integrator timeconstant proportional to R C which also determines the second dominanttime constant. It has been found that wide tolerances in motorparameters do not appreciably affect the performance of this servosystem. A high static, DC gain in the post-amplifier 14 provides smalldeadband at balance of the servo system. The third loop bandwidth isdefined as that frequency range over which the third loop acts as theinverse of its feedback provided by the RC network 24 and the capacitor30. In the system of FIG. 1, the third loop bandwidth may be expressedas (kC -,,,R ,C, )/(C (radians per second) where k is the velocity ofthe adjustable circuit element 18a at steady state for a given signalmagnitude applied to the motor 16. It can be seen by inspection of theforegoing. expression for third loop bandwidth that reducing capacitor Cincreases subsystem bandwidth.

Since post-amplifier integrator gain is inversely proportional to Cincreasing integrator gain increases the the third loop bandwidth. Bymaking the post-amplifier integrator gain sufficiently high, variationsin the bandwidth of the third loop have an inconsequential effect on theoverall system performance. In accordance with this invention, the thirdloop acts as integrator in the first loop for frequencies less than theloop three bandwidth. Under these conditions, it has been found thatwide tolerances in motor parameters do not ap preciably affect theperformance of the system. Rather, the dynamic performance of the systemis determined by the first dominant system time constant R C and thesecond dominant system time constant R C /K B where these time constantsare equal to l/m, for critical damping at the natural frequency (oFurthermore, high static or DC gain in the post-amplifier 14 providessmall deadband at balance of the system.

The first time constant may be derived by inspection. It is wellunderstood in the art that when an RC filter network such as the RCnetwork 24 acts upon the output of an amplifier such as the amplifier20, the inverse of the feedback transfer function of the high gainamplifier is the closed loop transfer function, in this case the firstdominant time constant R ,,C

Accordingly, the active RC filter network 24 is characterized by thefirst order equation where V is the voltage at the tap 18a, and V'stands for the time rate of change of V,,,,.

The second dominant time constant may be derived as follows: for signalbalance at the post-amplifier 14 assuming high post-amplifier integratorgain for signal balance at the summing point 10 by substitution ofequation (3) into equation (2) z ao Al/ 32) .r in) by multiplyingequation (4) by Rag/KA z'("32/ A1) a2+ 1- in and upon deriving equation5) by B R C /K B is the second dominant time constant. Thus, a theoutput of a first order system as expressed by equation (6) with aninput V is the output of embodiment of FIG. 1, the time constant(representing having a dominant time quantity (R R )C /k B.

These dominant time constants must still be equal to 1/0),, forcritically damped conditions at the natural frequency w I As in theembodiment of FIG. 1, the third loop acts as an integrator with respectto the second loop having an integrator time constant proportional tothe product (R R )C The post-amplifier integrator has an integratingtime constant proportional to the product (R R )C and preferably lessthan the integrator time constant for the third loop. 7

The following table specifies suitable values for the capacitors andresistors of FIGS. 1 and 2 for co equal to I radians per second:

System R;,, C C micro C R Type microfarads micro- FIG. No. farads (R=l0k) farads r /C 2 l 4 5000 l r /C 2 1 0 0 (Assumes 3 2 and R k) Itwill now be demonstrated that the system of FIG. 2 is equivalent to thesystem of FIG. 1. Since a capacitor acts as an open circuit at lowfrequencies, it is clear from inspection of FIG. 2 that the capacitor 30dominates the branch including the capacitor 30 and the resistor 40 andthat the capacitor 42 produces negligible shunting of the RC filternetwork including resistor 32a and 32b and the capacitor 42 at thepostamplifier input. As a result, the third loop acts as an integratoras it does in FIG. 1, and that the RC filter at the post-amplifier inputacts simply as a resistor with a value (R R (R R flmay equal R of FIG. 1to provide strict equivalence between the systems of FIGS. 1 and 2. Athigh frequencies, the capacitors 30 and 42 of FIG. 2 tend to act asshort circuits. Therefore the impedance of the branch including thecapacitor 30 and the resistor 40 is determined by the resistor 40 andthe RC filter at the input of the post-amplifier acts as an integrator.The combined effect of the RC filter and the third loop is that of anintegrator in the loop 1.

It hasbeen demonstrated that changes in motor parameters causenegligible variations in the system dynamic 7 characteristics. Thesystem exhibits other forms of insensitivity to parameter variationswhich may be understood from the following. A conventional DC motor, inparticular a DC motor with a permanent magnet field produces a velocityof the adjustable circuit means for a given DC motor input magnitudewhen the DC motor input is slowly time varying or of low frequency. Ittherefore introduces a lag in the forward path of the system. In fact,the motor may be considered to have an integrator gain, k At inputfrequencies that are sufficiently higher than the breakpoint frequency 1(radians)/'r,, see the motor produces an acceleration of the adjustablecircuit means and thereby introduces two lags. The post-amplifier in-'tegrator also introduces a lag. However, since the loop comprising themotor and post-amplifier acts as an integrator in loop two, only one lagis introduced in loop two even where a DC motor producing more than onelag, for slowly time varying DC motor input, is utilized. In thesituation where the one lag introduced into loop two, by loop three, ispredominant in loop two; i.e., the pre-amplifier and feedback network donot exhibit appreciable frequency dependent behavior, the pre-amplifiergain and/or feedback gain B may be varied over a wide range withoutcausing instability, since this only changes the second dominant timeconstant without introducing oscillatory behavior. Of course, the seconddominant system time constant is not affected. In another situation,another time constant may be included in loop two. For example, this maybe due to a reduced bandwidth of the preamplifier, or to another lagnetwork. This additional time constant may be provided in order toestablish another dominant system time constant. Thus, a third ordersystem withreduced sensitivity to parameter variations may beconstructed. This is because the pre-amplifier loop has a sensitivity toparameter variations of a single loop second order system instead ofthat of a single loop third order system.

Utilizing the same reference characters to identify the same elements,the system of FIG. 1 is shown in somewhat more detail in FIG. 3 asincluding a recorder pen 50 which is coupled to the adjustable circuitelement or slide-wire tap 18a and the motor 16. In addition to thecapacitor 30, the feedback path to the input of the post-amplifier 14also includes an inverter 52, a differentiating RC network 54 forderiving a velocity feedback signal, and a diode threshold network 56for providing large velocity signal damping. A current constraintfeedback path including diode threshold networks 58 and 60 is providedfor applying a feedback signal to the input of the pOst ampIifie'r 14thereby cohstraining current through the motor 16 to a tolerable level.Both the large signal velocity damping and the current constraintaspects of the system are more fully explained in copending applicationSer. No. 20,885, filed Mar. l9, 1970, and assigned to the assignee ofthis invention. Other means for maintaining balance at the input to thepost-amplifier so as to constrain the postamplifier output willoccur tothose of ordinary skill in the art.

Since the network 24 associated with the feedback amplifier 20 doesdifferentiate the position signal from the adjustable tap 18a, thefeedback-or restoring signal applied to the pre-amplifier 12 through aresistor 64 includes a velocity component and a position component. Therestoring signal is then compared with an input signal applied at afilter 66 which results in the generation of an error signal attheoutput of the preamplifier 12. Note the use of the adjustableresistance 67 which is connected to the input of the amplifier 12. Theadjustability of this resistance permits changes in both the span of thesystem and the gain of the amplifier without changing the sensitivity ofthe system as disclosed in copending application Ser. No. 20,880, filedMar. 9, 1970 and assigned to the assignee of this invention.

In FIG. 4, the system of FIG. 2 is embodied in a nullbalance recorder.Once again, identical reference characters are utilized to identify thesame elements.

Other modifications in the previously described systems are possible.For example, the low pass filter effect provided by the resistors 32aand 32b and the capacitor 42 of FIG. 2 may be provided by thepre-amplifier 12 by virtue of reduced bandwidth. Different motors 16 mayalso be utilized. For example, a linear motor with limited output travelmay be utilized to provide a controlled input to a mechanical amplifierwith a force and motion gain such as that shown in U.S. Pat. No.3,491,603. The DC motor may comprise an AC motor in combination with amodulator. The amplifier 14 in FIG. 1 may comprise a switching modepower output type amplifier. Details of one suitable switching modeamplifier are set forth in U.S. Pat. No. 3,384,833 I-Iitt which isassigned to the assignee of this inventron.

Although a second order system having two dominant time constants hasbeen described in the foregoing, this invention is not so limited. Forexample, the invention may also be practiced in a third order systemhaving an additional time constant at the input to the post-amplifierand in loop 2. B may also have frequency dependent characteristics.

In the embodiment of FIG. 5, the reactive means of the inner loopfeedback means comprises two capacitors 70 and 72 which provide tworeactive feedback paths to the input of the post-amplifier 14. Thecapacitor 70 which differentiates a position signal derived from the tap18a completes an inner velocity feedback loop via an inverting isolationamplifier 74 having one input connected to the tap 18a of the adjustablecircuit element through a resistor 75. The other input of the isolationamplifier 74 is connected to a junction 76 between two arms of a bridgecircuit 78 associated with the motor 16 where the motor 16 representsone arm of the bridge circuit. A tap 80 represents an intermediate pointin the resistive path comprised of resistors 80a to 800. As shown, thetap 80 is an adjustable junction between the opposite arms of the bridgecircuit. This is part of the inner acceleration feedback loop includingthe capacitor 72 where the capacitor 72 differentiates a velocity signalderived from the tap 80 to provide an acceleration feedback signalcomponent substantially free of the voltage drop across the motorresistance.

The position feedback by way of feedback network 22 to summing point issimilar to that shown in FIGS. 1 and 2. The preamplifier 12 shown inFIGS. 5, 6 and 7 may be either a voltage gain pre-amplifier or a currentgain pre-amplifier.

The current through the motor 16 must pass through the resistor 77 inorder to reach the return connection 88 of the output of the amplifier14. A voltage signal is developed at the return connection 88 withrespect to common 76, the magnitude of which is proportional to the IRdrop component of the motor voltage and polarity of which is opposite tothat of the IR drop.

The velocity signal component derived from the tap 80 of FIG. 5represents the motor voltage minus the signal proportional to the IRdrop. It will be appreciated that other circuit arrangements may beprovided to achieve a velocity proportional to the motor voltage minus asignal proportional to the IR drop which is utilized to obtain anacceleration feedback signal component substantially free of the IRmotor drop. For example, FIG. 5a shows a circuit arrangement wherein thecircuitry associated with the motor 16 comprises a current sensingresistor 140 and operational amplifiers 142 and 144. The amplifier 142which is connected across the terminals of the motor 16 produces anoutput signal representing motor voltage referred to circuit common 146.The operational amplifier 144 has an input connected to the currentsensing resistor 140 to produce an output signal representing aninverted motor current referred to circuit common. The motor voltagefrom the output of the amplifier 142 and the inverted motor currentsignal obtained from the output of amplifier 144 are then summed at asumming point 146 to obtain the velocity signal component.

The velocity signal component derived from the slidewire contact 18a viathe resistor 75, isolating amplifier 74 and capacitor may have analternate path shown in FIG. 5b. The isolating amplifier 74 is augmentedwith a capacitor 75c so that its output has both velocity and positionsignal components. Thus, the current through the capacitor 70 hasacceleration and velocity components. These components are combined withthe pre-amplifier 12 output by a summing amplifier 71. The accelerationcomponent of the part of the output due to the current through thecapacitor 70 is removed by a lag network comprised of resistors 73a and73b and capacitor 73. The inner loop feedback components that areapplied to the input of the postamplifier 14 are velocity andacceleration components due to the velocity signal derived from theslidewire contact 18a and the acceleration signal derived from contactas before.

The velocity, acceleration and motor voltage derivative feedback may beapplied to the input of the postamplifier 14 as shown in FIG. 5c. Thesefeedback signals are applied across weighting resistors and respectivewindings of transformer 79 so that the current that flows through eachwinding is proportional-to the derivative of its respective feedbackvoltage. The transformer 79 is of a type which produces a secondaryvoltage which is proportional to the sum of the primary currents. Thissecondary voltage is connected in series with the output voltage ofpre-amplifier 12 and the input port of amplifier 14.

The acceleration feedback signal of FIG. 5 may be derived by thealternate means shown in FIG. 5d. A low impedance motor current sensingprimary coil 148 of transformer 150 is placed in series with the motor.A high impedance primary coil 149 is connected between and returnconnection 88. The voltage across this coil is a good approximation ofthe motor voltage since the voltage across the current sensing coil 148is very low; thus, the secondary voltage across winding 151 isproportional to a weighted sum of motor current and motor voltage. Inaccordance with the invention, the phasing and number of turns of theprimary coils-is determined in such a way as to produce proper weightsso that the secondary voltage is a velocity signal just as the velocitysignal at contact 80 of FIG. 5. Of course the current sensing coil 148may be located on the opposite side of the motor 16. A variation of FIG.5d wherein the coil 149 is placed directly across the motor isacceptable if the impedance of coil 149 is sufficiently high so that thecurrent sensed by coil 148 is primarily the motor current. i

In the system shown in FIG. 5, the acceleration feedback gain (transferfunction) depends on the tachometric coefficient of the motor, ratherthan on the resistance of the motor. The DC motor has a back emf whichis generated at a given speed. A tachometric coefficient is defined, forpurposes of this invention, as the ratio of the back emf to the motorspeed. The velocity feedback gain depends on the adjustable circuitelement 18a. As a result, the ratio of the gains of the velocityfeedback loop (including the adjustable circuit element) and theacceleration feedback loop, is a stable quantity. This ratio representsthe subsystem bandwidth. Subloop bandwidth, as used herein, is definedas the frequency range over which a subloop acts as the inverse of itsfeedback transfer function.

System bandwidth, as used herein, is defined as the frequency rangecorresponding to the passband of the overall input output transferfunction. The subloop bandwidth lies between the system bandwidth andthe third subloop bandwidth of the embodiments shown in FIGS. 1 to 4.The stability of the subsystem bandwidth results in low sensitivity ofsystem dynamic performance to parameter variations. In addition, lowdeadband is achieved due to the fact that the capacitors 70 and 72provide capacitive feedback coupling rather than direct feedbackcoupling.

The existence of the acceleration feedback path through capacitor 72permits reduction of feedback gain in the path through branch 34. Thereare significant reductions in the delays in response for small errorsignals because of this reduced feedback gain. The derivative of themotor voltage feedback is minimized by maximizing the impedance of thebranch including the capacitor 38. A significant reduction in thefeedback of the motor voltage derivative is achieved because backlashand/or resilience (consequent resonant frequencies) do not exist in theacceleration feedback loop and consequently the acceleration feedbackloop has relatively high subloop bandwidth.

The system of FIG. 5 is embodied in a null-balance recorder similar toFIG. 3, in FIG. 6. Once again, identical reference characters areutilized to identify the same elements.

In FIG. 7, the reactive means of the inner feedback means comprises asingle capacitor 82. This capacitor 82 provides a reactive feedback loopfor both the velocity and acceleration feedback signal components. Avelocity signal is derived from the difference between the voltages attap 80 and motor terminal 76. A position signal is derived from thedifference between the voltages at contact 18a and terminal 18b of theadjustable circuit means. These signals appear in series and are appliedto the differential amplifier 74. The sum of the position signal and thevelocity signal appears at the output of amplifier 74 and the sum isdifferentiated by capacitor 82 deriving the velocity signal componentand acceleration signal component respectively. These signal componentscomprise the current through capacitor 82 which is combined with thecurrents through branch 34 and resistor 32 at the input of the amplifier14. As in the case of the embodiment shown in FIG. 5, the accelerationfeedback signal component which is obtained from differentiating avelocity signal derived directly from the motor 16 at the bridge circuit78 dominates the performance of the loop that it defines over a widefrequency range since the loop that it defines does not include thenonlinearities of the mechanical coupling means between the motor 16andthe adjustable circuit element 18. The dynamic performance of theacceleration loop depends on the tachometric coefficient of the motor 16over this wide frequency range. As a result, the bandwidth of thevelocity feedback loop has improved stability with respect to parametervariations. Also, the presence of acceleration feedback permits thereduction of the feedback of the motor voltage derivative therebyreducing the IR drop component which in turn reduces the delays inresponse for small error variations.

The dotted block labeled 7 in FIG. 5 is shown in considerably moredetail in FIG. 8 with a typical amplifier output current gain stage andits associated power supply shown explicitly. The output stage comprisesDarlington transistor pairs 83, 84 and 85, 86, connected for Class Boperation. The power supply 87 has a positive potential connected to thecollectors of the NPN transistors, a negative potential connected to thecollectors of the PNP transistors and a reference potential connected tothe bridge circuit 78 via the return connection 88. An independent powersupply 87 is used so that all of the motor current passes through theresistor 77 in order to produce a signal proportional to the motor IRdrop thereacross. Hence, a velocity signal is produced at the contactwith respect to the common terminal 76 which is at the same potential asan input terminal of the amplifier 81. The velocity signal isdifferentiated by the capacitor 72 in order to produce an accelerationfeedback signal as before. The resistor 81a connecting the output of theamplifier 81 to the output stage prevents excess current from flowingwhen the output stage saturates.

The dotted block labeled 7 in FIG. 5 may also be substituted by thecircuit shown in FIG. 9. In FIG. 9 the output stage is a switching modeamplifier. The amplifier 91 has differential outputs, 91a and 91b,connected to the inputs of OR gate 92. The output of the OR gate isconnected to an input of the pulse generator 93 in order to modulate thepulse generator pulse frequency and/or the pulse width as shown in U.S.Pat. No. 3,384,833 Hitt and assigned to the assignee of this invention.The output of the pulse generator 93 is connected to one of the inputsof AND gate 94 and one of the inputs of AND gate 95. The other input ofAND gate 94 is connected to amplifier output 91a and the other input ofAND gate 95 is connected to amplifier output 91b. Coincidence betweenthe proper polarity of the output of the amplifier 91 and the properbinary state of the output of the pulse generator 93 yields a uniqueoutput of an AND gate which causes a pulse to be delivered to the motorby way of switching transistors 96, 97 or 98, 99. The polarity of thepulse delivered to the motor is representative of the relative polarityof the differential outputs of amplifier 91. The capacitor 38 provides afeedback signal related to the derivative of the average motor voltage.As an alternative, a capacitor may be connected directly between themotor terminal 16a and sum point 15. However, averaging circuitry may berequired in this path. A special advantage is provided by the inventionbecause the capacitor 38 can be connected as shown in FIG. 9.Discrepancies between the motor voltage derivative and the feedbackthrough capacitor 38 are tolerable because the acceleration feedback isdominant insofar as the outer loops are concerned.

Another switching mode output stage, as shown in FIG. may be substitutedfor the dotted portion 7 of FIG. 5. This output stage is similar to thatof FIG. 9 except that a bridge type connection is employed for theswitching transistors. The power supply for the switching transistorbridge is shown as a two terminal power supply 108. This may be anadvantage in AC line operated instruments that are operated without atransformer. When a unique output occurs at the output of an AND gate, apulse of proper polarity is delivered to the motor. Suppose thatcoincidence of the proper polarity of the output of the amplifier 91 andthe binary state of the pulse generator exists so as to cause a uniqueoutput to occur from AND gate 94. This causes transistor 103 to turn ON.The proper polarity of the output of amplifier 91 causes transistor 104to turn ON completing a current path of one polarity. The other pair oftransistors 101, 102 operates in like manner, when a unique outputexists from the AND gate 95, to complete a current path of the oppositepolarity. It is apparent from the above discussion that the sense of themotor terminals with respect to the common 109 corresponds to thepolarity. Thus a differential amplifier connected across the motor and adifferential amplifier connected to resistor 77 are used to obtain motorvoltage and motor IR drop signals with respect to common 109. These twosignals combined by amplifier 107, cause an acceleration signal to passthrough capacitor 72 to sum point 15. A capacitor connected from theoutput of amplifier 105 to sum point is an alternative connection forcapacitor 38, similar to the alternative connection for this capacitorin the circuit of FIG. 9.

In accordance with the invention, the embodiments of FIGS. 9 and 10 havean acceleration feedback path from the motor via associated circuitry.The accelera tion feedback determines the bandwidth of the velocityfeedback inner loop. The capacitively coupled motor voltage feedbackfrom the output of the post-amplifier to its input has a secondaryeffect insofar as this bandwidth is concerned. In fact, the capacitivelycoupled motor voltage feedback can be minimized. This has verysignificant advantages for the following reasons. Most of the highfrequency components of the motor voltage pulses appear in the IR dropcomponent. When an acceleration feedback is derived from the motorvoltage via a prior art capacitively coupled feedback, special filteringmust be provided and/or additional dynamic range must be provided in theamplifiers or discrepancies may occur between the state of the motor andthe acceleration feedback when an approximate motor voltage signal priorto pulse modulation is used for feedback, such as the feedback throughcapacitor 38 in FIGS. 9 and 10. By utilizing the acceleration feedbackin accordance with the invention, the reduced capacitively coupled motorvoltage feedback yields reduced high frequency components ordiscrepancies can be tolerated because this acceleration feedback is thedominant feedback.

Various modifications in the network of FIGS. 1, 5, 7 and 9 may beutilized. For example, the reactive feedback means provided by thecapacitors 30, 32, 70, .72 and 82 may be provided by the reactivefeedback means shown in FIG. 1a as comprising a shunt inductor and aseries resistors 132. The reactive feedback means provided by thecapacitor 38 in combination with the resistor 36 in FIGS. 1 to 4 may beprovided a shunt inductor 138, a shunt resistor and series resistors142. A further modification of the embodiments of FIGS. 1 to 4 involvesthe use of a passive proportional plus derivative circuit shown in FIG.10. The passive circuit comprises a resistor 126 and a capacitor 128connected in series and a shunt resistor 129.

In the embodiments of FIGS. 5 to 7 except FIG. 5b, the velocity andacceleration feedback signal components are applied to a single node atthe input of the post-amplifier. In some instances, it may be desirableto apply the velocity and acceleration feedback signal components todifferent nodes. This will be the case where compensating networks areutilized to compensate for networks which establish desired systemdynamic performance characteristics. For example, an extradifferentiation in the velocity feedback path from the adjustablecircuit means may be compensated by an extra integrator between thepoint where the feedback of the velocity feedback path is applied andwhere the feedback of the acceleration feedback is applied shown as, forexample, in FIG. 5b. In any event, the signal components which areapplied to the post-amplifier will represent velocity and accelerationdue to the reactive means in the feedback paths.

Different motors 16 may also be utilized. For example, a two phase ACservomotor may be utilized in conjunction with a bridge connected to thecontrol winding as shown in FIG. 6-32 on page 242 of Control systemDesign, 2nd Edition, CJ. Savant, Jr., McGraw-Hill Book Company, 1958.The resulting AC velocity signal may be demodulated to provide a DCvelocity signal corresponding to the voltage at contact 80 in FIG. 6.

It will of course be understood that other modifications may be madewithout departing from the principles of the invention. The appendedclaims, are therefore, intended to cover any modification within thetrue spirit and scope of the invention.

a What is claimed:

1. An improved null-balance servo system for measuring an unknownelectrical quantity in the form of an input signal, said servo systemhaving a first loop providing overall system feedback and second andthird loops forming sub-loops within said first loop, said systemcomprising:

a means for producing an error signal related to the difference betweenan input signal and a signal for restoring balance to said system;

a DC pre-amplifier for amplifying said error signal;

a DC post-amplifier coupled to the output of said pre-amplifier;

an adjustable circuit element having an output coupled to said means forproducing an error signal;

a DC motor coupled between the output of said postamplifier and saidadjustable circuit element to generate said restoring signal in responseto movement of said adjustable circuit element;

a proportional plus derivative means coupled to the output of saidadjustable circuit element for producing a feedback signal including avelocity component, said last named means being interposed between saidadjustable circuit element and said means for producing an error signal,and reactive feedback means coupled between said proportional plusderivative means and the input of said post-amplifier to establish saidsecond and third loops, said second loop including said preamplifier,and said third loop including said postamplifier, said motor, saidadjustable circuit element, said proportional plus derivative means andsaid reactive means, said third loop acting like an integrator withrespect to said second loop.

2. The null-balance servo system of claim 1 wherein said post-amplifierincludes an output, a non-inverting input, and an inverting input andsaid null-balance servo system further comprises another reactivefeedback means from the output of said post-amplifier to the invertinginput of said post-amplifier, said post-amplifier and said reactivefeedback path acting like an integrator with an integrator gainsufficiently high for the third loop to act like an integrator withrespect to the second loop.

3. The null-balance servo system of claim 2 wherein a first integratortime constant for said third loop is proportional to said reactivefeedback means.

4. The null-balance servo system of claim 3 wherein a second integratortime constant for said post-amplifier in combination with said secondreactive feedback means is proportional to' said other reactive feedbackmeans, said integrator gain being inversely proportional to said secondintegrator time constant.

5. The null-balance servo system of claim 4 wherein said secondintegrator time constant is less than said first integrator timeconstant.

6. The null-balance servo system of claim 1 further comprising resistivemeans coupling the output of said pre-amplifier to the input of saidpost-amplifier.

7. The null-balance servo system of claim 6 wherein said reactivefeedback means includes a capacitive means.

8. The null-balance servo system of claim 7 including shunt capacitivemeans in combination with said resistive means to form a low pass filterat the input of said post-amplifier.

9. The null-balance servo system of claim 6 wherein said reactivefeedback means comprises inductive means.

10'. The null-balance servo system of claim 1 wherein said reactivefeedback means comprises capacitive means.

11. The null-balance servo system of claim 1 wherein said reactivefeedback means comprises inductive means.

12. The null-balance servo system of claim 1 wherein said proportionalplus derivative means comprises a feedback amplifier and lag network inthe feedback of said amplifier.

13. The null-balance servo system of claim 1 wherein said third loopincludes at least one integrator in cascade with said DC motor.

14. A high-speed null-balance servo system having optimal small signalresponse for measuring an unknown electrical quantity in the form of aninput signal comprising:

a means for producing an error signal related to the difference betweenan input signal and a signal for restoring balance to said system;

a DC pre-amplifier for amplifying said error signal;

a DC post-amplifier coupled to the output of said pre-amplifier;

an adjustable circuit element having an output coupled to said means forproducing an error signal;-

a DC motor connected to the output of said post-amplifier andmechanically coupled to said adjustable circuit element to generate saidrestoring signal in response to movement of said adjustable circuitelement;

a proportional plus derivative means coupled to the output of saidadjustable circuit element for producing a feedback signal including avelocity 7 component, said proportional plus derivative meansestablishing a first dominant system time constant; and I a reactivemeans coupling said feedback signal to the input of said post-amplifierso as to establish a second dominant system time constant proportionalto said reactive means.

15. The null-balance servo system of claim 14 wherein said firstdominant time constant established by said proportional plus derivativemeans and said second dominant system time constant established by saidreactive means are substantially equal.

16. A null-balance servo system having an optimal small signal responsefor measuring an unknown electrical quantity in the form of an inputsignal comprising: A v

a means for producing an error signal relating to the difference betweenan input signal and an overall feedback signal for restoring balance tosaid system; a DC preamplifier for amplifying said error signal; a DCpost-amplifier coupled to the output of said pre-amplifier;

a means for producing feedback signals comprising a DC motorandassociated circuitry connected to the output of said post-amplifier andan adjustable circuit element mechanically coupled to said motor;

an outer loop feedback means coupling said adjustable circuit element ofsaid means for producing feedback signal to said means for producing anerror signal so as to apply said overall system feedback signal to saidmeans for producing an error signal; and

an inner loop feedback means including reactive means for coupling saidmeans for producing feedback signals to the input of said post-amplifierand applying a velocity feedback signal component to the input of saidpost-amplifier and an acceleration feedback signal component to theinput of said post-amplifier, said acceleration feedback signalcomponent being substantially free of the voltage drop across the motorresistance.

17. The system of claim 16 wherein said means for producing feedbacksignals further comprises a proportional plus derivative means connectedto the output of said adjustable circuit element, said outer loopfeedfeedback means comprises a first reactive feedback path from saidadjustable circuit element to said postamplifier for said velocitysignal component and a second reactive feedback path from saidassociated circuitry of said DC motor to said post-amplifier for saidacceleration signal component.

21. The system of claim 20 wherein said associated circuitry comprises abridge including said motor as an arm in said bridge, said secondreactive feedback path being connected to said bridge.

22. The system of claim 19 wherein said reactive means of said innerloop feedback means comprises a single reactive feedback path coupled tosaid adjustable circuit element and said associated circuitry of saidmotor.

23. The system of claim 16 further comprising a phase switching circuitwherein said associated circuitry comprises switching transistorscoupled to and controlled by said switching circuit for providing aswitch mode operation of said motor.

24. An improved null-balance servo system for measuring an unknownelectrical quantity in the form of an input signal having an overallpositional feedback loop, a velocity feedback inner loop and anacceleration feedback inner loop of high sub-loop bandwidth forsignificantly reducing the effect of variations of motor resistance andsignificantly reducing the effect of variations of motor torquesensitivity, comprising:

means for producing an error signal relating to the difference betweenan input signal and an overall feedback signal for restoring balance tosaid system;

a DC pre-amplifier for amplifying said error signal;

a DC post-amplifier coupled to the output of said pre-amplifier;

means for producing feedback signals including a DC motor having anelectrical input connected to the output of said post-amplifier, and anadjustable circuit element having a mechanical input coupled to themechanical output of said motor and a variable electrical outputproducing an overall positional feedback signal;

overall positional feedback loop means coupling the output of saidadjustable circuit element to the input of said pre-amplifier; and

inner loop feedback means coupling the output of said adjustable circuitelement in said velocity feedback inner loop and said motor electricalinput to the input of said post-amplifier in said acceleration feedbackinner loop so as to respective- 1y apply a velocity feedback signalcomponent and an acceleration feedback signal component to the input ofsaid post-amplifier, said acceleration feedback signal component beingsubstantially independen of the voltage drop across the motorresistance.

25. The system of claim 24 wherein said means for producing feedbacksignals further comprises a bridge wherein said motor forms one leg ofsaid bridge on one side of said bridge, said inner loop feedback meansincluding a reactive means coupled to a terminal on the opposite side ofsaid bridge so as to applysaid acceleration feedback signal component tothe input of said post-amplifier.

26. The system of claim 24 wherein said means for producing feedbacksignals further comprises a differential amplifier means and animpedance connected in series with said motor for generating a signalrepresenting the voltage drop across the motor resistance, saiddifferential amplifier means coupled to said motor and said impedancefor generating a velocity signal representative of the motor voltageminus the voltage drop across the motor resistance, said inner loopfeedback means including reactive means coupling the output of saiddifferential amplifier means to the input of said post-amplifier toapply said acceleration feedback signal component to the input of saidpost-amplifier.

27. The system of claim 24 wherein said means for producing feedbacksignals further comprises a plurality of interconnected switchingtransistors and pulse generating means having an output coupled to saidpost-amplifier and an input coupled to said switching transistors forgenerating a pulsed output from said switching transistors which is afunction of the output from said post-amplifier, said pulsed outputbeing applied to said motor.

28. The system of claim 27 wherein said means for producing saidfeedback signal further comprises a bridge wherein said motor forms oneleg of said bridge, said inner loop feedback means including reactivemeans coupled between said bridge and the input of said post-amplifierso as to apply said acceleration feedback signal component to the inputof said postamplifier.

29. The system of claim 27 wherein said switching transistors form abridge, said means for producing said feedback signals furthercomprising an impedance connected in series with said motor and acrosssaid bridge and differential amplifier means coupled to said motor andsaid impedance for generating a velocity signal representative of themotor voltage minus the voltage drop across the motor impedance, saidinner loop feedback means including a reactive means coupling the outputof said differential amplifier to the input of said post-amplifier forapplying said acceleration signal components thereto.

' -sss-I v 1 v I Y K v 9 33" UNlfl l-lj) S'IA'II'ISlA'll'lN'l OFFICECE-R'LIFICAIE 01F CORRECTION YatcntNO- 3,73 v .nma :Max 8,197; I v l o OInventor) Samuel- J. MacMullan If: .is certified that error appears inthe above-*idcntificd patent and that said Letters Patent are herebycorrected as shown below:

Column l line 56, "balance" should read --unhalan'ce--.

. Column 3 line 14, "in" should read ---is---'.

I Q I e Column one (k C R )/C I should read 3o 26 28 3s m)--. I

. I 4 n v u 1 I I. I Column 6, lane 14,. R C /K B shouldread v R c /k- BI Column 6, line 47, equation (4) the openinqparenthesis before "a s"has .been omitted.

1 I ,I Y" Column 6, llne 51, equation .(5) f'e (r /K should read v Y .7I xn m)".

Column 7, I line 11,. after "time" insert --1':on'satant Column 7, lines25-30, table should appear as follows:

System R C C C R Type miQrom rofarads mfiro- (Figure No.) 1 l T farads(R =l0k) arads' a l 2 m/ 38 .2 o 1 4 v 5000 1 I 2 1 w Q Signedand sealedthis 2nd day of Jul'y I QH.

(SEAL)- Attest:

EDWARD M.FL'ET( ZHER,JR. c. MARSHALL: :bANLN Attestlng ,Ofhcer-Commissioner. of Patents uses-1 f 1 00-0000 uNrms-iu s'r/mcs PATENT0001c;

i. clm'xwviclrrls O1-"COK1USCTION Patent No. 3,752,070 I macaw I I l I 9Samuel J. MaoMullan 1nvcntor(s) It .is' certified that error appears inthe above-identified patent and that said Letters Patent are herebycorrected as shown below:

Column 1,. line 56, "balance" should read -+-unbalance-. Column 3, lineI4, "in" should read -is-'.

I 7 I Column 5, l ne 62 (kC R C )/C should read Column '6, "line 47,equation (4) the opening parenthesis before has been omitted. v Q Column6, line 51, equation (5) I 0 x n m).

Column 7, v line 1 1,. after 1"tiine" insert ,--oonstant---.

Column 7, lines 25-30, table should appear as follows:-

. s stem R c c c v R Type m2r om rofarads m aro- 1 (Figure No.) A. 1farads (R =l0k) farad's] j 2 m/ -38. .2 1 3 '4 1 5000 Signe d and sealedthis 2nd day of July 1914.

smu- AtteSt EDWARD M.FLETCHER,JR. c. MARSHALL: 130 120 Attesting Officerv Commissioner. of Patents Column 6, lane 14,. R C /K B shouldread I R clk e e u n should read

1. An improved null-balance servo system for measuring an unknownelectrical quantity in the form of an input signal, said servo systemhaving a first loop providing overall system feedback and second andthird loops forming sub-loops within said first loop, said systemcomprising: a means for producing an error signal related to thedifference between an input signal and a signal for restoring balance tosaid system; a DC pre-amplifier for amplifying said error signal; a DCpost-amplifier coupled to the output of said pre-amplifier; anadjustable circuit element having an output coupled to said means forproducing an error signal; a DC motor coupled between the output of saidpost-amplifier and said adjustable circuit element to generate saidrestoring signal in response to movement of said adjustable circuitelement; a proportional plus derivative means coupled to the output ofsaid adjustable circuit element for producing a feedback signalincluding a velocity component, said last named means being interposedbetween said adjustable circuit element and said means for producing anerror signal, and a reactive feedback means coupled between saidproportional plus derivative means and the input of said post-amplifierto establish said second and third loops, said second loop includingsaid pre-amplifier, and said third loop including said post-amplifier,said motor, said adjustable circuit element, said proportional plusderivative means and said reactive means, said third loop acting like anintegrator with respect to said second loop.
 2. The null-balance servosystem of claim 1 wherein said post-amplifier includes an output, anon-inverting input, and an inverting input and said null-balance servosystem further comprises another reactive feedback means from the outputof said post-amplifier to the inverting input of said post-amplifier,said post-amplifier and said reactive feedback path acting like anintegrator with an integrator gain sufficiently high for the third loopto act like an integrator with respect to the second loop.
 3. Thenull-balance servo system of claim 2 wherein a first integrator timeconstant for said third loop is proportional to said reactive feedbackmeans.
 4. The null-balance servo system of claim 3 wherein a secondintegrator time constant for said post-amplifier in combination withsaid second reactive feedback means is proportional to said otherreactive feedback means, said integrator gain being inverselyproportional to said second integrator time constant.
 5. Thenull-balance servo system of claim 4 wherein said second integrator timeconstant is less than said first integrator time constant.
 6. Thenull-balance servo system of claim 1 further comprising resistive meanscoupling the output of said pre-amplifier to the input of saidpost-amplifier.
 7. The null-balance servo system of claim 6 wherein saidreactive feedback means includes a capacitive means.
 8. The null-balanceservo system of claim 7 including shunt capacitive means in combinationwith said resistive means to form a low pass filter at the input of saidpost-amplifier.
 9. The null-balance servo system of claim 6 wherein saidreactive feedback means comprises inductive means.
 10. The null-balanceservo system of claim 1 wherein said reactive feedback means comprisescapacitive means.
 11. The null-balance servo system of claim 1 whereinsaid reactive feedback means comprises inductive means.
 12. Thenull-balaNce servo system of claim 1 wherein said proportional plusderivative means comprises a feedback amplifier and lag network in thefeedback of said amplifier.
 13. The null-balance servo system of claim 1wherein said third loop includes at least one integrator in cascade withsaid DC motor.
 14. A high-speed null-balance servo system having optimalsmall signal response for measuring an unknown electrical quantity inthe form of an input signal comprising: a means for producing an errorsignal related to the difference between an input signal and a signalfor restoring balance to said system; a DC pre-amplifier for amplifyingsaid error signal; a DC post-amplifier coupled to the output of saidpre-amplifier; an adjustable circuit element having an output coupled tosaid means for producing an error signal; a DC motor connected to theoutput of said post-amplifier and mechanically coupled to saidadjustable circuit element to generate said restoring signal in responseto movement of said adjustable circuit element; a proportional plusderivative means coupled to the output of said adjustable circuitelement for producing a feedback signal including a velocity component,said proportional plus derivative means establishing a first dominantsystem time constant; and a reactive means coupling said feedback signalto the input of said post-amplifier so as to establish a second dominantsystem time constant proportional to said reactive means.
 15. Thenull-balance servo system of claim 14 wherein said first dominant timeconstant established by said proportional plus derivative means and saidsecond dominant system time constant established by said reactive meansare substantially equal.
 16. A null-balance servo system having anoptimal small signal response for measuring an unknown electricalquantity in the form of an input signal comprising: a means forproducing an error signal relating to the difference between an inputsignal and an overall feedback signal for restoring balance to saidsystem; a DC pre-amplifier for amplifying said error signal; a DCpost-amplifier coupled to the output of said pre-amplifier; a means forproducing feedback signals comprising a DC motor and associatedcircuitry connected to the output of said post-amplifier and anadjustable circuit element mechanically coupled to said motor; an outerloop feedback means coupling said adjustable circuit element of saidmeans for producing feedback signal to said means for producing an errorsignal so as to apply said overall system feedback signal to said meansfor producing an error signal; and an inner loop feedback meansincluding reactive means for coupling said means for producing feedbacksignals to the input of said post-amplifier and applying a velocityfeedback signal component to the input of said post-amplifier and anacceleration feedback signal component to the input of saidpost-amplifier, said acceleration feedback signal component beingsubstantially free of the voltage drop across the motor resistance. 17.The system of claim 16 wherein said means for producing feedback signalsfurther comprises a proportional plus derivative means connected to theoutput of said adjustable circuit element, said outer loop feedbackmeans being coupled to the output of said proportional plus derivativemeans.
 18. The system of claim 17 wherein said inner loop feedback meansis also coupled to the output of said proportional plus derivativemeans.
 19. The system of claim 16 wherein said inner loop feedback meansis coupled to said associated circuitry of said DC motor and saidadjustable circuit element so as to apply said velocity and accelerationfeedback signal components to the input of said post-amplifier.
 20. Thesystem of claim 19 wherein said inner loop feedback means comprises afirst reactive feedback path from said adjustable circuit element tosaid post-amplifier for said velocity signal component And a secondreactive feedback path from said associated circuitry of said DC motorto said post-amplifier for said acceleration signal component.
 21. Thesystem of claim 20 wherein said associated circuitry comprises a bridgeincluding said motor as an arm in said bridge, said second reactivefeedback path being connected to said bridge.
 22. The system of claim 19wherein said reactive means of said inner loop feedback means comprisesa single reactive feedback path coupled to said adjustable circuitelement and said associated circuitry of said motor.
 23. The system ofclaim 16 further comprising a phase switching circuit wherein saidassociated circuitry comprises switching transistors coupled to andcontrolled by said switching circuit for providing a switch modeoperation of said motor.
 24. An improved null-balance servo system formeasuring an unknown electrical quantity in the form of an input signalhaving an overall positional feedback loop, a velocity feedback innerloop and an acceleration feedback inner loop of high sub-loop bandwidthfor significantly reducing the effect of variations of motor resistanceand significantly reducing the effect of variations of motor torquesensitivity, comprising: means for producing an error signal relating tothe difference between an input signal and an overall feedback signalfor restoring balance to said system; a DC pre-amplifier for amplifyingsaid error signal; a DC post-amplifier coupled to the output of saidpre-amplifier; means for producing feedback signals including a DC motorhaving an electrical input connected to the output of saidpost-amplifier, and an adjustable circuit element having a mechanicalinput coupled to the mechanical output of said motor and a variableelectrical output producing an overall positional feedback signal;overall positional feedback loop means coupling the output of saidadjustable circuit element to the input of said pre-amplifier; and innerloop feedback means coupling the output of said adjustable circuitelement in said velocity feedback inner loop and said motor electricalinput to the input of said post-amplifier in said acceleration feedbackinner loop so as to respectively apply a velocity feedback signalcomponent and an acceleration feedback signal component to the input ofsaid post-amplifier, said acceleration feedback signal component beingsubstantially independent of the voltage drop across the motorresistance.
 25. The system of claim 24 wherein said means for producingfeedback signals further comprises a bridge wherein said motor forms oneleg of said bridge on one side of said bridge, said inner loop feedbackmeans including a reactive means coupled to a terminal on the oppositeside of said bridge so as to apply said acceleration feedback signalcomponent to the input of said post-amplifier.
 26. The system of claim24 wherein said means for producing feedback signals further comprises adifferential amplifier means and an impedance connected in series withsaid motor for generating a signal representing the voltage drop acrossthe motor resistance, said differential amplifier means coupled to saidmotor and said impedance for generating a velocity signal representativeof the motor voltage minus the voltage drop across the motor resistance,said inner loop feedback means including reactive means coupling theoutput of said differential amplifier means to the input of saidpost-amplifier to apply said acceleration feedback signal component tothe input of said post-amplifier.
 27. The system of claim 24 whereinsaid means for producing feedback signals further comprises a pluralityof interconnected switching transistors and pulse generating meanshaving an output coupled to said post-amplifier and an input coupled tosaid switching transistors for generating a pulsed output from saidswitching transistors which is a function of the output from saidpost-amplifier, said pulsed output being applied to said motor.
 28. Thesystem of claim 27 wherein said means for producing said feedback signalfurther comprises a bridge wherein said motor forms one leg of saidbridge, said inner loop feedback means including reactive means coupledbetween said bridge and the input of said post-amplifier so as to applysaid acceleration feedback signal component to the input of saidpost-amplifier.
 29. The system of claim 27 wherein said switchingtransistors form a bridge, said means for producing said feedbacksignals further comprising an impedance connected in series with saidmotor and across said bridge and differential amplifier means coupled tosaid motor and said impedance for generating a velocity signalrepresentative of the motor voltage minus the voltage drop across themotor impedance, said inner loop feedback means including a reactivemeans coupling the output of said differential amplifier to the input ofsaid post-amplifier for applying said acceleration signal componentsthereto.